Since the building of the great modern art museums in New York, Paris and London, the narrative of 20th-century and contemporary art has been told, by and large, through the stories of the great European and North American cities.

But the Tate has announced it is time to look further afield. "There is not a crisis in British or European art," said the Tate director, Sir Nicholas Serota, "but we are conscious art is being made across the world and those areas outside Europe and North America cannot be regarded as the periphery."

Tate will reflect its new international focus through a two-year programme of activities focused on Africa, beginning on 24 November. Events will include performance works in the new Tate Tanks by Nigerian artist Otobong Nkanga and Angolan Nástio Mosquito. Next year, Tate Modern will show an extensive work that it has recently acquired by the artist Meschac Gaba, from Benin. Titled Museum of Contemporary African Art 1997-2002, and in 12 sections or "rooms", it acts as a playful, questioning museum – while highlighting that there is, in fact, no such thing as a museum of contemporary African art.

In the summer of 2013 Tate Modern will also show Britain's first major exhibition of work by Ibrahim El-Salahi, who was born in Sudan, studied at the Slade in London, and returned to Sudan in the 1970s where he was wrongfully imprisoned. He lived in exile in Qatar and is now settled in Oxford, his work mingling European modernist influences with Arabic, African and Islamic visual ideas.

"We are recognising that we need to collect across the world. There is no one single centre for modern and contemporary art and it certainly isn't London or New York," said Serota. Chris Dercon, director of Tate Modern, added: "The way art history has been written over the past decades has been through a focus on national histories. We are trying to broaden that and show an international history of art."

For the past decade, Tate has been actively collecting from outside Europe and North America. In 2002, a collecting committee – consisting of Tate curators and private collectors – was founded to pursue art from Latin America. This has been gradually followed by committees focusing on Asia-Pacific, the Middle East and North Africa, South Asia, Russia and eastern Europe, and Africa.

Frances Morris, who heads Tate's international activities, described the committees as "rather like exclusive book clubs" containing "like-minded people" who may be originally from the region focused on. Each member, who may become part of the committee by invitation, pays £10,000 to sit on the body, money that then supports the acquisition budget of each committee, which is otherwise drawn from sources including Tate's government grant-in-aid, its endowment, and its Friends' scheme. Individual committee members may donate further to support individual purchases. The Tate spends £4m-5m a year on acquiring art, of which just under £2m is spent by the international acquisition committees.

Serota ruled out the creation of Tate "franchises" overseas, but emphasised the reciprocal nature of its relations with institutions overseas. The museum has, for example, recently signed a memorandum of agreement with the Pinacoteca in São Paulo aimed at co-creating exhibitions, and sharing expertise and research. Brazil in particular has a burgeoning art scene, with increasingly important art fairs and biennales; there was a highly visible cohort of both Brazilian dealers and Brazilian collectors at last month's Frieze art fair in London.

He denied that the Tate could stand accused of a neocolonial programme of removing the best art from the countries it was produced in. Elvira Dyangani Ose, a curator who specialises in African art at Tate, said: "It is important for African art to be part of a major international narrative. We are not taking everything out of Africa; but we need to tell the whole story of modernity."

Serota also announced the signing of a memorandum of understanding between the Sultanate of Oman and Tate. In 2010, the museum organised an exhibition of British art to celebrate the 40th anniversary of the sultan's accession. The sultan has donated £2m to the Tate and the institution is helping Oman to create its new national museum in Muscat.